\(\mathcal {D}_{tr}\) denotes the training set; \(\ell (\cdot , \cdot )\) denotes the cross entropy loss.
It can be shown [1]} that, if \(\mathbf {\pi }(\cdot )\) and \(\mathbf {f}_r(\cdot ; \mathbf {\theta }_r)\) both have sufficient representation power, the globally optimal \(\mathbf {\pi }(\mathbf {X})\) of Equation (REF ) would generate masks \(\mathbf {M}\) that are globally optimal under Equation (REF ).
